Mister Exam

Other calculators

The derivative of the function/ sin^2(y)

Derivative of sin^2(y)

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   2   
sin (y)
$$\sin^{2}{\left(y \right)}$$ 
sin(y)^2
Detail solution

  1. Let .

  2. Apply the power rule: goes to

  3. Then, apply the chain rule. Multiply by :

    1. The derivative of sine is cosine:

    The result of the chain rule is:

  4. Now simplify:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
2*cos(y)*sin(y)
$$2 \sin{\left(y \right)} \cos{\left(y \right)}$$
Simplify
The second derivative [src] 
  /   2         2   \
2*\cos (y) - sin (y)/
$$2 \left(- \sin^{2}{\left(y \right)} + \cos^{2}{\left(y \right)}\right)$$
Simplify
The third derivative [src] 
-8*cos(y)*sin(y)
$$- 8 \sin{\left(y \right)} \cos{\left(y \right)}$$
Simplify
    © Mister Exam – Calculator